Here is one way to write the same letter three times: n + n + n. Is there a neater way to write three of the same letter added together?
Take three hands-up answers, not open call-outs. Listen for a pupil who offers 3n — revoice it, but don't confirm the rule yet; that lands in Watch and Notice.
Think of each x as a bag with an unknown number of cubes inside, and each plain number as loose cubes on the table.
Watch three expressions get tidied up. Each board is captioned with the algebra it is showing, so you can see the bags and the expression at the same time.
Key point Only like terms can be combined. Bags join with bags because they hold the same unknown amount. Loose numbers join with loose numbers. A bag and a loose number are not like terms, so they can never be pushed together into one term.
Before each answer appears, predict which terms are alike and which have to stay apart.
Work the three expressions on the board, grouping like terms as the class predicts. Between the three expressions, turn-and-name a pupil to say the group before you reveal each answer, so the beat keeps moving.
Sort the scattered cards into two groups. Put the x-bags (the x-terms) in one place. Put the loose cubes (the plain numbers) in the other. The cards on screen are 5x, 2, 3x, x and 4. When they are sorted, say the simplified expression aloud.
Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud.
Use counters or cube-and-bag cards at pupils' desks so everyone sorts as the board is sorted. Watch for a pupil who tries to slide a loose number into the x-bag pile — that is the misconception to surface. Can a plain 4 ever hide inside a bag we can't count?
The x-terms are 5x + 3x + x, which make 9x; the loose cubes are 2 + 4, which make 6. Once the cards are grouped (9x in the x-bags, 6 in the loose cubes), lead the class to state the simplified expression as 9x + 6.
In your maths copy, simplify each of these expressions by collecting like terms. Before you combine anything, underline the like terms in matching colours — all the x-terms one colour, all the plain numbers another.
Write the simplified expression at the end of each line.
Walk the room glancing at the colour underlining before pupils combine — this is whole-class copybook practice, not marking. Catch anyone who writes a single term like 6x from 4x + 3 + 2x; the loose 3 must survive.
Sort every card into its group: x-terms with x-terms, plain numbers with plain numbers. Only like terms go together.
When the cards are sorted, say the whole simplified expression out loud and write it in your copy. Both parts, so 7x + 3, not just 7x. The board checks the sorting; you supply the expression.
The sets get harder: two x-terms and one number, then two x-terms and two numbers, then three x-terms and two numbers. Predict how many x-bags and how many loose cubes each set will end with before you press Check.
This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
After each Check, ask the class to state the simplified expression in full (both groups), so the answer is 7x + 3, not just 7x.
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